Algebraic Techniques For Signal Processing And Coding

Abstract

This talk will survey the role of algebraic fields in general and of the Fourier transform in particular in the engineering problems of digital signal processing and of error control codes. The premise of the talk is that there are close ties between the subjects of digital signal processing and of error control codes. For a variety of reasons, the subject of error control codes has been highly algebraic. The use of algebraic methods has developed more slowly in digital signal processing. By surveying the computational procedures, we hope to stimulate new methods and applications. The plan of the talks is to survey the structure of useful algebraic fields, then examine the Fourier transform in an arbitrary field. Finally, we shall discuss the role of algebraic fields and of Fourier transforms in a variety of applications. From a computational point of view, the algorithms used in digital signal processors and in error correcting decoders are often quite similar. From an applications point of view it may be inefficient to separate these two tasks into distinct subsystems of an implementation. The future may very well see a blurring of the line between the traditional tasks of filtering and the traditional tasks of error control. Indeed, both of these tasks, broadly stated, involve the removal of noise from a received signal.